Literature Cited
S. V. Uspenskii, “Embedding theorems for weighted classes,” Trudy Mat. In-ta. Akad. Nauk SSSR,60, 282–303 (1961).
S. L. Sobolev, “Density of functions with compact support in L lP (En),” Sibirsk. Matem. Zh.,4, No. 3, 673–682 (1963).
V. R. Pormnov, “Two embedding theorems for the space L (1)pb (ω×R+) with applications,” Dokl. Akad. Nauk SSSR,155, No. 4, 761–764 (1965).
V. N. Sedov, “Embedding theorems with an arbitrary weight in metrics of the type L (1)pb (ω×R+),” Diploma Treatise, MFTI (1965).
V. N. Sedov, “Functions which become polynomials at ∞,” Proceedings of the All-Union Symposium on Embedding Theory [in Russian], Baku (1966).
Yu. S. Nikol'skii, “Boundary properties of functions in weighted classes,” Dokl. Akad. Nauk SSSR,164, No. 3, 503–506 (1965).
T. S. Pigolkina, “Density of functions with compact support in weighted classes,” Matem. Zametki,2, No. 1, 53–60 (1967).
O. V. Besov, “Extension of functions in L lp and W lp ,” Trudy. Mat. In-ta, Akad. Nauk SSSR,89, 5–17 (1967).
O. V. Besov, “Behavior of differentiable functions at infinity and density of functions with compact support,” Trudy Mat. In-ta. Akad. Nauk SSSR,105, 3–14 (1969).
L. D. Kudryatsev, “Parametric inequalities for functions of several variables,” Dokl. Akad. Nauk SSSR,202, No. 6, 1261–1264 (1972).
L. D. Kudryatsev, Properties of Boundary Values of Functions in Weighted Spaces and Their Applications to Boundary Value Problems [in Russian], Nauka, Moscow (1972).
L. D. Kudryatsev, “Traces of functions of several variables and direction fields which are regular at infinity for the Laplace operator,” Trudy Mat. In-ta. Akad. Nauk SSSR,112, 256–270 (1972).
P. I. Lizorkin, “Generalized Liouville differentiation and the method of multipliers in embedding theory for differentiable functions,” Trudy Mat. In-ta. Akad. Nauk SSSR,105, 89–167 (1969).
L. Schwartz, Theorie des Distributions I, II, Herman, Paris (1950/51).
S. V. Uspenskii, “Diffrerential properties of solutions of a class of pseudodifferential equations at infinity,” Sibirsk. Matem. Zh.,13, No. 3, 665–678 (1972).
P. Kree, “Sur les multiplicateur dans FL p1 ,” Comptes Rendus,260, No. 7, 4400–4403 (1965).
O. V. Besov, V. P. Il'in, and P. I. Lizorkin, “Lp-estimates for a class of nonisotopically singular integrals,” Dokl. Akad. Nauk SSSR,169, No. 6, 1250–1253 (1966).
G. H. Hardy, J. E. Littlewood, and G. Polya, Inequalities, Cambridge University Press (1952).
L. A. Lyusternik and V. I. Sobolev, Elements of Functional Analysis [in Russian], Nauka, Moscow (1965).
S. V. Uspenskii, “Representation of functions which are determined by a class of hypoellipic operators,” Trudy Mat. In-ta. Akad. Nauk SSSR,117, 292–299 (1972).
P. I. Lizorkin, “(Lp, Lq)-multipliers of Fourier integrals,” Dokl. Akad. Nauk SSSR,152, No. 4, 808–811 (1963).
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Translated from Sibirskii Matematicheskii Zhurnal, Vol. 16, No. 5, pp. 1053–1070, September–October, 1975.
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Uspenskii, S.V., Chistyakov, B.N. The transition to polynomials upon convergence of |x|→∞ for solutions of a class of pseudodifferential equations. Sib Math J 16, 806–819 (1975). https://doi.org/10.1007/BF00967111
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DOI: https://doi.org/10.1007/BF00967111